Collective Behavior of Urease pH Clocks in Nano- and Microvesicles Controlled by Fast Ammonia Transport

The transmission of chemical signals via an extracellular solution plays a vital role in collective behavior in cellular biological systems and may be exploited in applications of lipid vesicles such as drug delivery. Here, we investigated chemical communication in synthetic micro- and nanovesicles containing urease in a solution of urea and acid. We combined experiments with simulations to demonstrate that the fast transport of ammonia to the external solution governs the pH–time profile and synchronizes the timing of the pH clock reaction in a heterogeneous population of vesicles. This study shows how the rate of production and emission of a small basic product controls pH changes in active vesicles with a distribution of sizes and enzyme amounts, which may be useful in bioreactor or healthcare applications.


Urease-encapsulated nanovesicles
The lipid film hydration and extrusion method was used to produce DPhPC + Rh-DOPE (0.5 mol%) liposomes of approximately 200 nm diameter. The phospholipid DPhPC was found to give more reproducible results in initial experiments with urease encapsulated in nanovesicles than palmitoyloleyl-phosphatidylcholine (POPC) used with the microvesicles. 1 DPhPC + Rh-DOPE thin films were formed by adding 300 μL of lipid in chloroform to a glass vial and drying overnight under vacuum.
Hydrating solutions (1.0 mL) of different composition were used depending on the desired vesicle encapsulants for each experiment: for example, pyranine (0 or 20 mM), urease (Type III, 5.45 mg ml -1 = 220 U ml -1 ) and HCl to adjust to the desired starting pH (e.g. 0.1 mM HCl for pH 4.0). Following vortex mixing, the samples were subjected to ten cycles of freeze-thawing (nine cycles at 45°C, and the final cycle at 36°C) to improve encapsulation efficiency. 2 It was verified that urease did not undergo significant degradation under these conditions. The samples were then extruded eleven times through a polycarbonate filter of pore size 200 nm to produce large unilamellar vesicles of approximately 200 nm, confirmed by Dynamic Light Scattering (DLS). Unencapsulated urease and pyranine were removed from the external medium by size-exclusion chromatography (Sephadex G50 medium) with a mobile phase corresponding to the pH of the encapsulated media (e.g. 0.1 mM HCl for pH 4.0) to produce a solution of nano-vesicles. The Rh-DOPE was used to visually track the vesicles in the column.
For Jack Bean urease Type III (Sigma-Aldrich) used in the experiments, the typical specific activity is 40 U mg -1 where 1 unit (U) = 1 µmol NH 3 min -1 at pH 7 and 25 ˚C. The molecular mass is M r = 545 kDa (hexamer with Ni 2+ included). 3 A concentration of 5.45 mg mL -1 (or 220 U mL -1 ) corresponds to 10 μM urease assuming pure enzyme. However, Type III contains impurities including phosphates from the purification process: purified urease has reported specific activities of >600 U mg -1 (Sigma-Aldrich Type C3) to 6000 U mg -1 (depending on the conditions of the assay e.g. temperature 20 -38 ˚C, nature of buffer and pH). 4,5 So the mass of urease in a Type III sample may be estimated from the ratio of the specific activity to pure, taken here as 40/600 x 100% = 6.7%, to give [E] = 0.7 µM. The encapsulation efficiency is <100% using the lipid hydration method, so this represents an upper limit in concentration. 6  min at 210°C. The test tubes were then removed and allowed to cool for 5 min, before addition of 3.9 mL deionised water, 500 µL of 2.5% w/v ammonium molybdate (VI) tetrahydrate solution, and 500 µL of 10% w/v ascorbic acid solution. Each test tube was vortexed, and capped with parafilm, before being returned to the heating block for 7 minutes at 100°C. The test tubes were removed from the heating block and allowed to cool to room temperature. The absorbance of each calibration standard and test sample was measured at 820 nm using a Cary 100 UV-vis spectrometer. A calibration curve was created from the standards and used to determine the phosphorous concentration of the liposome samples.

Calibration curve for pH
A calibration curve was produced for the indicator pyranine as a function of pH using a Cary 100 UV-Vis spectrophotometer. Pyranine exhibits a pH-dependent absorption and fluorescence spectrum and has been used for determination of pH in vesicles. 7,8 The protonated form (PyOH 3-) has a λ max at 405 nm and the deprotonated form (PyO 4-) at 457 nm ( Figure S1). The ratio of absorbance, A, or fluorescence, F, of pH indicators at two wavelengths can be related to the concentration of free acid and the acid dissociation constant K a . 9, 10 For pyranine: where R is the ratio of absorbances: A 450 /A 405 , R min and R max are the asymptotic limits of the curve at low and high pH (R min is the ratio of absorbance of the protonated species (PyOH 3-) at the two wavelengths, R max is the ratio of absorbance of the deprotonated form (PyO 4-) and K a ' is the apparent dissociation constant of pyranine which takes into account an additional absorbance factor. Ratiometric measurements were used to ensure the data is independent of the concentration of fluorophore and we used the ratio of absorbances here rather than ratio of fluorescences as the calibration curve was found to be more sensitive to changes in pH at higher pH, giving a more accurate determination of the final pH of the pH clock reaction. However the absorbance measurements resulted in greater error at low pH.
A phosphate-citrate buffer, covering a pH range of 4.0 -8.0, and a glycine-NaOH buffer, covering a pH range of 8.6 -10.6, were used to produce the calibration curve. The absorbance of each buffered solution containing pyranine (50 μM) and deionised water-encapsulating liposomes of approximate diameter 200 nm at a phosphorus content of 250 µM was measured at room temperature. A fit to the data was obtained in OriginPro using the equation: y = a + (b -a)/(1 + 10 d*(c -x) ) from SE2 with the addition of the parameter d to give a better fit to the data at low pH as the presence of liposomes resulted in an x-axis offset ( Figure S1(b)). The (apparent) pH was determined from SE3: pH = c -(1/d)log((y -b)/(a -y)) and, using the formula for the propagation of errors, the error in the pH, s pH , was related to the error in R (s y ): s pH = (s y 2 ((y -b)/(y -a) 2 -1/(y -a)) 2 (y -a) 2 )/(d 2 (y -b) 2 )) 1/2 /ln(10).

Estimation of number of vesicles
The total number of lipids per vesicle is given by the surface area of the inner and outer monolayers of the unilamellar vesicle divided by the head group of a single lipid molecule: where D is the diameter of the vesicle and h is the bilayer thickness. The estimated (outer) volume of the vesicle was ~ V j = 4.2 x 10 -12 µL and the vesicle volume fraction was estimated as = NV i /V o = 2 x 10 -3 , with total volume of vesicles = 1.0 µL.

Nanovesicle Kinetic data analysis
Vesicle solutions were diluted to 500 µM lipid concentration. A volume of 250 µL was placed in a 550 µL micro-cuvette (2 x 3.5 mm window, path length 10 mm) and 250 µL urea (100 mM) in hydrochloric acid solution was added to initiate the reaction. Measurements were typically collected using a Cary 100 UV-Vis spectrophotometer every minute for the first 60 minutes then every five minutes for each kinetic run. All experiments were performed at room temperature (20 ± ˚C).
The data was analysed using OriginPro. Representative curves for individual runs with different acid concentration are shown in Figure S2(a). In order to determine a clock reaction time, a Hill fit was produced of the absorption ratio, R = A 450 /A 405 , in time, t, for each kinetic run: R = a + (b -a)t n / (k n +t n ) where k = width at half max, a is the minimum absorption ratio, b = the maximum ratio absorption. The pH in time ( Figure S2  In order to determine whether any unencapsulated enzyme from, for example, burst vesicles, in the solution could influence the reaction, a control experiment was performed in which surfactant Triton-X was added to lyse the vesicles. Upon addition of Triton-X to the solution, with vesicles and urea no change in absorbance was observed ( Figure S3), demonstrating that the total amount of enzyme contained in the vesicles was insufficient to catalyse the reaction once diluted in outer solution. Triton-X added to rupture the vesicles. Vesicles were prepared with hydrating solution: urease (220 U ml -1 ), HCl (0.2 mM) and pyranine (20 mM) and placed in a microcuvette to which a solution of urea (100 mM) and HCl (0.4 mM) was added to initiate the reaction.
Data was collected from three independent experiments for each value of the initial concentrations. The mean ratio of absorbance, R, was determined in time and the corresponding standard errors were calculated for Figure 1(b) and the mean value of R was used to determine the pH and error in pH for Figure 1(c). The error in the pH was determined using propagation of errors, using the standard error of the ratio of absorbance. The mean and standard error of T c were determined from the Hill fit of the three independent experiments. The initial and final value of the pH at 5 mins and 90 mins were determined from the value of R from the fitted relationship and equation 3. The initial pH data was taken at 5 mins to avoid the influence of initial mixing of the urea solution and the vesicles but was also unreliable as a result of the large error at low pH ( Figure S4).

Urease-encapsulated microvesicles
The microvesicles were prepared using a water-in-oil (w/o) emulsion droplet transfer method, which typically produces a population of giant unilamellar vesicles (GUV) of sizes 1 -100 µm. 12 Vesicles were prepared with a solution of urease Type III (40.3 U mg -1 ) at 80 U mL -1 or 2.0 mg mL -1 .
With M r = 545 kDa = 545 x 10 3 g mol -1 , this corresponds to 3.7 µM assuming pure enzyme, however, Type III contains impurities: pure urease has reported specific activities of >600 -6000 U mg -1 (depending on the conditions of the assay, temperature, nature of buffer and pH). 4,14 So, the mass of urease in a sample may be estimated as 40/600 x 100% = 6.7%, to give [E] = 0.25 µM.

Confocal Imaging
Images of the vesicles were obtained with a Leica TCS SP8 confocal microscope with a 20X objective

Calibration curve for pH
Lipid vesicles containing different pH buffer solutions and pyranine (50 µM) were prepared to obtain a pH calibration curve. The range of pH between 4.6 and 8.2 was covered with a citrate-phosphate buffer, where R is the ratio of fluorescence, and the pH is given by (SE3): pH = c + log(R -a)/(b -R). There S12 are some structural differences in the microvesicles (eg surface attached lipids, formation of multisomes) that likely contribute to the error in the ratio of fluorescence at a given pH.

Estimation of number of vesicles
A tile scan was performed of the entire reactor chamber and the total number of vesicles was of the order of N = 3 x 10 4 which is a lower estimate of the total amount of vesicles It was noted that there was some spatial variation in density. In a typical kinetic run, images were obtained every 40 s, hence it was impractical to monitor the whole reaction chamber, and 0.4 mm x 0.4 mm images were obtained. Thus, to establish a representative number density in a typical kinetic run, the number and diameter of vesicles from images of nine separate kinetic runs was determined using MATLAB, with a radius bigger than 5 pixels (2 µm). The data was used to produce a probability mass function for the vesicle diameter ( Figure   2a)

Microvesicle Kinetic Data Analysis
The reaction chamber was constructed using a transparent silicone sheet (MXBAOHENG, thickness

Modelling of the urea-urease reaction in vesicles
The system was modelled as a set of coupled ordinary differential equations (ODEs) describing the rate of change of species in the vesicles and the external solution, hence assuming the solutions are wellmixed on the length scales considered. Diffusion is fast compared to reaction in the vesicles: the diffusion timescale of ammonia in a 20 µm vesicle, with a diffusion coefficient of 2 × 10 -3 mm 2 s -1 at 298 K, 15 is t = L 2 /D = 0.2 s. On greater length scales, the urease reaction can support propagating pH fronts in thin layers of solution with speeds of the order of 0.5 mm min -1 , providing the total enzyme concentration is above a threshold amount (> 1 U ml -1 at pH 4). 16 The rate of change of pH in experiments was generally much slower than in our earlier work and there was no evidence of pH fronts in the experiments presented here, probably because the vesicle volume fraction was too low.
The main processes in the model are

Enzyme catalysed reaction
The enzyme catalysed hydrolysis of urea produces ammonia and carbon dioxide: Substrate and product inhibition terms were included: K s = equilibrium constant for uncompetitive substrate inhibition and K p = equilibrium constant for non-competitive product inhibition.
The urease enzyme Type III (Sigma-Aldrich) used in experiments is not pure and has specific activity of 40 U mg -1 (1 unit = 1 µmol NH 3 min -1 at pH 7 and 25 °C) compared to 600 -6000 U mg -1 of pure urease. In order to facilitate comparison of the simulations with experiments, we used U mL -1 for the enzyme concentration: where s is the specific activity and m is the mass concentration of Type III, in mg mL -1 . The concentration of urease, [E] T , in M, can be estimated from the activity of Type III relative to the activity of pure urease, p, and the molecular mass of Jack Bean urease, M r = 545000 g mol -1 : Then the maximum enzyme rate, v max , in M s -1 , is given by: So to account for the enzyme concentration in U mL -1 ; [ ] 1 We set k 1 = k cat /p/M r so that k cat [E] T = k 1 [E] where [E] is in U ml -1 and (as mg g -1 is equivalent to ml L -1 ) k 1 has units of M U -1 ml s -1 . Turnover numbers for Jack Bean urease are reported as k cat = (1 -90) × 10 3 s -1 (pH 5.5 -8 and 15 -38 ˚C). 4,18,19 We took k 1 = 3.6 × 10 -6 M U -1 ml s -1 in line with our earlier S17 work 20 under nonbuffered conditions at 20 ˚C and with p = 600 U mg -1 (Sigma-Aldrich Type C3), k cat = 1.2 × 10 3 s -1 .
Experiments with urease encapsulated in egg lecithin liposomes suggested that there was no change in the maximal enzyme rate as a result of the encapsulation under buffered conditions, 6 and variation of the enzyme constants did not have a significant effect on the overall trends reported here. The values of all the enzyme constants are given in Table 1.

Equilibria
The pH inside and outside the vesicles is determined by the following reversible reactions: The acid equilibria rate constants are well established. 21 The pyranine pK a varies depending on the ionic strength. 22

Transfer rates and permeability
The transfer of species across the membrane boundary was assumed to follow a simple solubilitydiffusion mechanism: Where J i is the flux of the solute species i, P i is the permeability coefficient (m s -1 ) that depends on the nature of the membrane and the chemical species, and ΔC is the concentration drop across a membrane of thickness L. The rate of change of concentration in a spherical vesicle of surface area A and volume V was thus: 23 The permeability coefficients are related to the diffusion coefficient and partition coefficient of the species in the organic phase. The transfer of neutral species: urea, ammonia, carbon dioxide and acetic acid were included here. The values of the permeability coefficients given in the literature vary depending on the method of determination and may be hindered by unstirred layer effects. 24 We set P NH3 = 1 × 10 -4 m s -1 , and P CO2 = 1 × 10 -6 m s -1 and P Urea = 1 × 10 -8 m s -1 , broadly in line with literature values. 25,26 The permeability of acetic acid was taken as P HA = 1 × 10 -7 m s -1 . 27 Permeability coefficients of neutral species are unlikely to vary greatly between the two lipids of similar carbon chain length (POPC and DPhPC) used here.
The transfer of ionic species and large species was assumed to be negligible on the timescale of the experiment (~ 1 hour). Proton permeability is controversial and has wide ranging values reported from 10 -11 -10 -3 m/s. 28 Proton transport may involve a fast initial component that is quickly balanced by formation of an electrical gradient. Here, the permeability of protons, (P H+ ) was taken as zero.

S19
We did not take into account osmosis in these simulations. In general, we did not observe significant change in volume of the vesicles during the course of an experiment with microvesicles, however water flow may contribute to some of the behaviour and will be explored in future work.

Equations and parameters for populations of vesicles in solution
In the vesicles, the rate of change of concentration of a species A i is determined by the reaction rate and net transfer rate (where applicable):  Table 1. The rate equations were solved using XPPAUT with integration method STIFF. 29 The ode file for the models used in the simulations presented here are included in the Appendix.

Homogeneous population
The XPPAUT file is given in Appendix, model 1. The buffering effect of pyranine on the urease pH clock reaction in a vesicle, with no mass transfer, is seen in Figure S8(a). The concentration of urea is reduced by less than 2% as a result of the pH switch in the vesicles, thus the reaction is not at equilibrium at T = 90 min ( Figure S8(b)).

S21
(a) The pH time profile is shown in Figure S9(a) for the reaction in vesicles at three different initial acid concentrations and the corresponding clock time, T c , (to pH = 6.75) and initial (5 min) and final pH (90 min) as a function of acid concentration are shown in Figure S9    however here our main aim is to determine the influence of enzyme distribution on the collective dynamics so the form of the distribution was not further explored. 30 The vesicle volume fraction was estimated as = NVi/Vo = 2 x 10 -3 , with total volume of vesicles = 1.0 µL. In order to simulate a population of 2.4 × 10 11 nanovesicles, the number of enzyme molecules (X*P*2.4x10 11 ) in the corresponding volume (P*1 µL) was used to calculate the average enzyme concentration in U ml -1 (1 mol L -1 = 3.14 x 10 8 U ml -1 ) for that volume fraction. The rate of change of Ao was given by:

Heterogeneous population
where w j is the fraction of the vesicle volume with a given enzyme number/concentration.

Microvesicles
The XPPAUT file is given in Appendix, model 3. The initial conditions in the microvesicles were: In order to simulate a population of microvesicles with different enzyme amount and sizes for Figure   6, a bivariate histogram of X = 30 bins was taken with weighting factor w j,k for the fraction of vesicles in each bin: where w j,k was calculated from the dot product of a normal probability distribution for the enzyme in the vesicles and the experimental probability distribution for the vesicle sizes ( Figure 6). The values of w j,k are included in the ode file. The enzyme concentration was varied from X = 60 -100 U ml -1 , with mean = 80 and sd = 10. A normal distribution was used as in a sample volume of 114 vesicles, the volume was 1.9 × 10 -4 µL and there were 2.6 × 10 6 urease molecules with [E] = 0.25 µM and an average of 2.3 × 10 5 molecules per vesicle. Again we note that large variations in intravesicle solute concentration have been reported, however our goal here was to observe the influence of heterogeneity on the collective dynamics, rather than quantitatively match experimental results, so we do not explore the nature of the distribution further here. 30 The pH in time, vesicle diameter and corresponding clock time and initial and final pH are shown in Figure S11. The initial pH was influenced by both the enzyme content (yellow circles) and the diameter, with a smaller diameter and smaller enzyme concentration favouring low pH.

S25
The average T c and initial and final pH for the population of vesicles with changes in the concentration of initial acid are shown in Figure S12